Rational points on certain quintic hypersurfaces

Maciej Ulas

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Dopo aver ricordato i principali risultati concernenti l'unirazionalità dell'ipersuperficie quartica generale $X_{4}$ di $P^{n}$ (definita su un corpo K qualsiasi) si illustra la costruzione geometrica che permette di provare l'esistenza di una superficie razionale in ogni $X_{4}$ di $P^{n}$ , con $n \geq 4$ , e di trovare altri esempi di ipersuperficie quartiche lisce che sono unirazionali oltre a quello dato da B. Segre nel 1960. Si mostra poi come l'analisi delle superficie quartiche monoidali (cioè contenenti un punto...